A statistics professor has office hours from 9am to 10am each day. The number of

Question

A statistics professor has office hours from 9am to 10am each day. The number of students waiting to see the professor is a random variable, X, with the probability distrubution shown below.

P(X=0)=0.05

P(X=1)=0.10

P(X=2)=0.40

P(X=3)=0.25

P(X=4)=0.15

P(X=5)=0.05

The professor gives each student 10 minutes. Determine the probability that a student arriving just after 9 will have to wait no longer than ten minutes to see the professor. (Think carefully)                                                                                                                                                                                                                                                                                     

Explanation / Answer

The professor gives each student 10 minutes.

Hence, if the student arriving just after 9 will have to wait no longer than 10 minutes,ie., the student has to wait maximum 10 minutes is when there is at most(maximum) one student.

Therefore, the probability of atmost 1 student is given as P(X<1) = P(X=0) + P(X=1)

P(X=0) = 0.05

P(X+!) = 0.10

Hence, P(X < 1) = 0.05 + 0.10 = 0.15

That is the probability that a student arriving just after 9 will have to wait no longer than ten minutes to see the professor is 0.15.

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